A scalar Volterra derivative for the $PoU$-integral

V. Marraffa

Abstract: A weak form of the Henstock Lemma for the $PoU$-integrable functions is given. This allows to prove the existence of a scalar Volterra derivative for the $PoU$-integral. Also the $PoU$-integrable functions are characterized by means of Pettis integrability and a condition involving finite pseudopartitions.